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Volume
Volume, also called capacity, is a quantification http://en.wikipedia.org/wiki/Quantification of how much space http://en.wikipedia.org/wiki/Space an Object (philosophy) http://en.wikipedia.org/wiki/Object_%28philosophy%29 occupies. The international unit for volume is the cubic meter. Explained The volume of a solid object is a numerical value given to describe the three-dimensional http://en.wikipedia.org/wiki/Dimension concept of how much space it occupies. One-dimensional objects (such as line (mathematics)http://en.wikipedia.org/wiki/Line_%28mathematics%29) and two-dimensional objects (such as square (geometry)s http://en.wikipedia.org/wiki/Square_%28geometry%29) are assigned zero volume in the three-dimensional space. Mathematically Mathematically, volumes are defined by means of integral calculus http://en.wikipedia.org/wiki/Integral_calculus, by approximating the given body with a large amount of small cubes or concentric cylinder (geometry)|cylindrical]] shells, and adding the individual volumes of those shapes. The generalization of volume to arbitrarily many dimensions is called content http://en.wikipedia.org/wiki/Content. In differential geometry http://en.wikipedia.org/wiki/Differential_geometry, volume is expressed by means of the volume form http://en.wikipedia.org/wiki/Volume_form. Word difference Volume and capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in litres or its derived units), and volume being how much space an object displaces (commonly measured in cubic metres or its derived units). In thermodynamics Volume is a fundamental parameter in thermodynamics and it is conjugate to pressure. Volume formulae The volume of a parallelepiped is the absolute value of the scalar triple product of the subtending vectors, or equivalently the absolute value of the determinant of the corresponding matrix. The volume of any tetrahedron, given its vertices a''', '''b, c''' and '''d, is (1/6)·|det(a'−'b, b'−'c, c'−'d)|, or any other combination of pairs of vertices that form a simply connected graph. Volume measures: other metric units A commonly used called metric unit for volume is the litre (American spelling liter), and one thousand litres is the volume of a cubic metre (American spelling cubic meter), which was formerly termed a stere and often called a "cube" in engineering slang. A cubic centimetre (American spelling cubic centimeter) is the same volume as a millilitre. Volume measures: USA U.S. customary units of volume: *U.S. fluid ounce, about 29.6 mL *U.S. liquid pint = 16 fluid ounces, or about 473 mL *U.S. dry pint = 1/64 U.S. bushel, or about 551 mL (used for things such as blueberries) *U.S. liquid quart = 32 fluid ounces or two U.S. pints, or about 946 mL *U.S. dry quart = 1/32 U.S. bushel, or about 1.101 L *U.S. liquid gallon = 128 fluid ounces or four U.S. quarts, about 3.785 L *U.S. dry gallon = 1/8 U.S. bushel, or about 4.405 L *U.S. (dry level) bushel = 2150.42 cubic inches, or about 35.239 L The acre foot is often used in measuring the volume of water in a reservoir or an aquifer. It is the volume of water that would cover an area of one acre to a depth of one foot. It is equivalent to 43,560 cubic feet or exactly 1233.481 837 547 52 m³. *cubic inch = 16.387 064 cm3 *cubic foot = 1,728 in3 ≈ 28.317 dm3 *cubic yard = 27 ft3 ≈ 0.7646 m3 *cubic mile = 5,451,776,000 yd3 = 3,379,200 acre-feet ≈ 4.168 km3 Volume measures: UK Imperial units of volume: *UK fluid ounce, about 28.4 mL (this equals the volume of an avoirdupois ounce of water under certain conditions) *UK pint = 20 fluid ounces, or about 568 mL *UK quart = 40 ounces or two pints, or about 1.137 L *UK gallon = 160 ounces or four quarts, or exactly 4.546 09 L May it be noted that due to metrication within the UK, the quart is now obsolete and the fluid ounce extremely rare. The gallon is only used for transportation uses, (it is illegal for petrol & diesel to be sold by the gallon). The pint is the only Imperial unit that is in everyday use, for the sale of draught beer & cider (bottled & canned beer is sold in SI units) and for milk (this too is increasingly being sold in SI units). Relationship to density The volume of an object is equal to its mass divided by its average density. This is a rearrangement of the calculation of density as mass per unit volume. The term specific volume is used for volume divided by mass. This is the reciprocal of the mass density, expressed in units such as cubic meters per kilogram (m³•kg−1). Volume comparisons To help compare different volumes, see orders of magnitude (volume)http://en.wikipedia.org/wiki/Orders_of_magnitude_%28volume%29 See also *Conversion of units#Volume http://en.wikipedia.org/wiki/Conversion_of_units#Volume *Orders of magnitude (volume)http://en.wikipedia.org/wiki/Orders_of_magnitude_%28volume%29 *mass *density Category:Chemistry Category:Physics Category:Measurement